what is the length of the missing leg? if necessary, round to the nearest tenth. a = kilometers

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $c^{2}=a^{2}+b^{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the legs. Here, $c = 9.8$ km and one leg $b = 9.4$ km. We want to find $a$, so $a=\sqrt{c^{2}-b^{2}}$.

Step2: Substitute values

$a=\sqrt{(9.8)^{2}-(9.4)^{2}}=\sqrt{(9.8 + 9.4)(9.8 - 9.4)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). First, calculate $9.8+9.4 = 19.2$ and $9.8 - 9.4=0.4$. Then $a=\sqrt{19.2\times0.4}=\sqrt{7.68}$.

Step3: Calculate the square - root and round

$\sqrt{7.68}\approx2.8$ km.

Answer:

$2.8$